Question and Answers Forum

All Questions      Topic List

Others Questions

Previous in All Question      Next in All Question      

Previous in Others      Next in Others      

Question Number 60756 by readone97 last updated on 25/May/19

express in partial fraction 5/(x−2)(x+3)^2

$${express}\:{in}\:{partial}\:{fraction}\:\mathrm{5}/\left({x}−\mathrm{2}\right)\left({x}+\mathrm{3}\right)^{\mathrm{2}} \\ $$

Commented by Prithwish sen last updated on 25/May/19

(1/((x−2)(x+3)^2 )) =(A/((x−2))) +(B/((x+3))) +(C/((x+3)^2 ))  and then proceed.

$$\frac{\mathrm{1}}{\left(\mathrm{x}−\mathrm{2}\right)\left(\mathrm{x}+\mathrm{3}\right)^{\mathrm{2}} }\:=\frac{\mathrm{A}}{\left(\mathrm{x}−\mathrm{2}\right)}\:+\frac{\mathrm{B}}{\left(\mathrm{x}+\mathrm{3}\right)}\:+\frac{\mathrm{C}}{\left(\mathrm{x}+\mathrm{3}\right)^{\mathrm{2}} } \\ $$$$\mathrm{and}\:\mathrm{then}\:\mathrm{proceed}. \\ $$

Answered by ajfour last updated on 25/May/19

(5/((x−2)(x+3)^2 ))=(a/(x−2))+(b/(x+3))+(c/((x+3)^2 ))  a=(5/((x+3)^2 ))∣_(x=2) =(1/5)  c=(5/((x−2)))∣_(x=−3) = −1  now in first line let x=0  ⇒ −(5/(18))= −(5/2)+(b/3)−(1/9)  ⇒ b=3(((45+2−5)/(18)))=7  hence   (5/((x−2)(x+3)^2 ))= (1/(5(x−2)))+(7/(x+3))−(1/((x+3)^2 )) .

$$\frac{\mathrm{5}}{\left({x}−\mathrm{2}\right)\left({x}+\mathrm{3}\right)^{\mathrm{2}} }=\frac{{a}}{{x}−\mathrm{2}}+\frac{{b}}{{x}+\mathrm{3}}+\frac{{c}}{\left({x}+\mathrm{3}\right)^{\mathrm{2}} } \\ $$$${a}=\frac{\mathrm{5}}{\left({x}+\mathrm{3}\right)^{\mathrm{2}} }\mid_{{x}=\mathrm{2}} =\frac{\mathrm{1}}{\mathrm{5}} \\ $$$${c}=\frac{\mathrm{5}}{\left({x}−\mathrm{2}\right)}\mid_{{x}=−\mathrm{3}} =\:−\mathrm{1} \\ $$$${now}\:{in}\:{first}\:{line}\:{let}\:{x}=\mathrm{0} \\ $$$$\Rightarrow\:−\frac{\mathrm{5}}{\mathrm{18}}=\:−\frac{\mathrm{5}}{\mathrm{2}}+\frac{{b}}{\mathrm{3}}−\frac{\mathrm{1}}{\mathrm{9}} \\ $$$$\Rightarrow\:{b}=\mathrm{3}\left(\frac{\mathrm{45}+\mathrm{2}−\mathrm{5}}{\mathrm{18}}\right)=\mathrm{7} \\ $$$${hence}\: \\ $$$$\frac{\mathrm{5}}{\left({x}−\mathrm{2}\right)\left({x}+\mathrm{3}\right)^{\mathrm{2}} }=\:\frac{\mathrm{1}}{\mathrm{5}\left({x}−\mathrm{2}\right)}+\frac{\mathrm{7}}{{x}+\mathrm{3}}−\frac{\mathrm{1}}{\left({x}+\mathrm{3}\right)^{\mathrm{2}} }\:. \\ $$

Terms of Service

Privacy Policy

Contact: info@tinkutara.com